2x^2=37x-35

Solution for 2x^2=37x-35 equation:

2x^2=37x-35

We move all terms to the left:

2x^2-(37x-35)=0

We get rid of parentheses

2x^2-37x+35=0

a = 2; b = -37; c = +35;
Δ = b2-4ac
Δ = -372-4·2·35
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-33}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+33}{2*2}=\frac{70}{4}
=17+1/2
$