$$\frac{3\pm-5}{02}-\frac{4t+5}{5}=\frac{3}{4}+t$$
$t=\frac{5\left(3±\left(-5\right)\right)}{18}-\frac{35}{36}$
$$10\left(3±\left(-5\right)\right)-4\left(4t+5\right)=15+20t$$
$$10\left(3±\left(-5\right)\right)-16t-20=15+20t$$
$$10\left(3±\left(-5\right)\right)-16t-20-20t=15$$
$$10\left(3±\left(-5\right)\right)-36t-20=15$$
$$-36t-20=15-10\left(3±\left(-5\right)\right)$$
$$-36t=15-10\left(3±\left(-5\right)\right)+20$$
$$-36t=35-10\left(3±\left(-5\right)\right)$$
$$-36t=-10\left(3±\left(-5\right)\right)+35$$
$$\frac{-36t}{-36}=\frac{-10\left(3±\left(-5\right)\right)+35}{-36}$$
$$t=\frac{-10\left(3±\left(-5\right)\right)+35}{-36}$$
$$t=\frac{5\left(3±\left(-5\right)\right)}{18}-\frac{35}{36}$$
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