2x^2=15x+7

Solution for 2x^2=15x+7 equation:

2x^2=15x+7

We move all terms to the left:

2x^2-(15x+7)=0

We get rid of parentheses

2x^2-15x-7=0

a = 2; b = -15; c = -7;
Δ = b2-4ac
Δ = -152-4·2·(-7)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{281}}{2*2}=\frac{15-\sqrt{281}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{281}}{2*2}=\frac{15+\sqrt{281}}{4}
$