(8x+15)(6x+2)+(7x+10)(8x+15)=0

Solution for (8x+15)(6x+2)+(7x+10)(8x+15)=0 equation:

(8x+15)(6x+2)+(7x+10)(8x+15)=0

We multiply parentheses ..

(+48x^2+16x+90x+30)+(7x+10)(8x+15)=0

We get rid of parentheses

48x^2+16x+90x+(7x+10)(8x+15)+30=0

We multiply parentheses ..

48x^2+(+56x^2+105x+80x+150)+16x+90x+30=0

We add all the numbers together, and all the variables

48x^2+(+56x^2+105x+80x+150)+106x+30=0

We get rid of parentheses

48x^2+56x^2+105x+80x+106x+150+30=0

We add all the numbers together, and all the variables

104x^2+291x+180=0

a = 104; b = 291; c = +180;
Δ = b2-4ac
Δ = 2912-4·104·180
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(291)-99}{2*104}=\frac{-390}{208}
=-1+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(291)+99}{2*104}=\frac{-192}{208}
=-12/13
$