2x2-6x=4x+7

Solution for 2x2-6x=4x+7 equation:

2x^2-6x=4x+7

We move all terms to the left:

2x^2-6x-(4x+7)=0

We get rid of parentheses

2x^2-6x-4x-7=0

We add all the numbers together, and all the variables

2x^2-10x-7=0

a = 2; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·2·(-7)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*2}=\frac{10-2\sqrt{39}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*2}=\frac{10+2\sqrt{39}}{4}
$